Digraph and matrix approach for risk evaluations under Pythagorean fuzzy information

Failure Mode and Effects Analysis (FMEA) is an effective framework that is extensively utilized to determine and eradicate the possible failures from substances, structures, designs, services or organizations. The traditional risk evaluating methods have been criticized because of reasons that include disregard for correlative significance of risk factors, complicated multiplications, and lack of exactness and accuracy in the evaluations. In this paper, the effectiveness of traditional techniques is improved by a novel approach to analyze risks in FMEA that makes use of digraphs and matrix techniques under the Pythagorean fuzzy environment. We begin by defining triangular Pythagorean fuzzy numbers. We use them to express both the linguistic terms and all other data and information regarding the risk factors (inclusive of occurrence, severity, and detection). Then a Pythagorean fuzzy digraph captures the interrelations connecting the risk factors and the relative significance among them. Finally, we form the corresponding Pythagorean fuzzy risk matrices for every identified failure mode, and we calculate the risk priority indexes in order to identify the risk priorities. We also study an example of a steam valve system in a power generating plant as an illustrative application of our model.

Automated summary

This study improves the effectiveness of traditional FMEA techniques by using digraphs and matrix techniques under the Pythagorean fuzzy environment. By defining triangular Pythagorean fuzzy numbers, constructing Pythagorean fuzzy digraphs, and forming corresponding Pythagorean fuzzy risk matrices, a novel approach to identify risk priorities is proposed. An illustrative application of the model is demonstrated through the analysis of a steam valve system in a power generating plant.